Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

A lifting-linearization method based on the Koopman operator and Dual Faceted\nLinearization is applied to the control of a robotic excavator. In excavation,\na bucket interacts with the surrounding soil in a highly nonlinear and complex\nmanner. Here, we propose to represent the nonlinear bucket-soil dynamics with a\nset of linear state equations in a higher-dimensional space. The space of\nindependent state variables is augmented by adding variables associated with\nnonlinear elements involved in the bucket-soil dynamics. These include\nnonlinear resistive forces and moment acting on the bucket from the soil, and\nthe effective inertia of the bucket that varies as the soil is captured into\nthe bucket. Variables associated with these nonlinear resistive and inertia\nelements are treated as additional state variables, and their time evolution is\nrepresented as another set of linear differential equations. The lifted linear\ndynamic model is then applied to Model Predictive Contouring Control, where a\ncost functional is minimized as a convex optimization problem thanks to the\nlinear dynamics in the lifted space. The lifted linear model is tuned based on\na data-driven method by using a soil dynamics simulator. Simulation experiments\nverify the effectiveness of the proposed lifting linearization compared to its\ncounterpart.\n